Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem

Nicos Christofides
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Nicos Christofides: Carnegie-Mellon University

SN Operations Research Forum, 2022, vol. 3, issue 1, 1-4

Abstract: Abstract An O(n3) heuristic algorithm is described for solving d-city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition. The algorithm involves as substeps the computation of a shortest spanning tree of the graph G defining the TSP and the finding of a minimum cost perfect matching of a certain induced subgraph of G. A worst-case analysis of this heuristic shows that the ratio of the answer obtained to the optimum TSP solution is strictly less than 3/2. This represents a 50% reduction over the value 2 which was the previously best known such ratio for the performance of other polynomial growth algorithms for the TSP.

Date: 2022
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DOI: 10.1007/s43069-021-00101-z

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